Question Number 139577 by bemath last updated on 29/Apr/21 $$\:\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{number}\frac{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{2}}+\frac{\left(\mathrm{y}−\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{4}}+\frac{\left(\mathrm{z}−\mathrm{3}\right)^{\mathrm{2}} }{\mathrm{6}}+\mathrm{3}=\mid\mathrm{x}−\mathrm{1}\mid+\mid\mathrm{y}−\mathrm{2}\mid+\mid\mathrm{z}−\mathrm{3}\mid\: \\ $$ Answered by mr W last updated on 29/Apr/21 $${a}=\mid{x}−\mathrm{1}\mid\geqslant\mathrm{0},\:{b}=\mid{y}−\mathrm{2}\mid\geqslant\mathrm{0},\:{c}=\mid{z}−\mathrm{3}\mid\geqslant\mathrm{0} \\…
Question Number 74042 by liki last updated on 18/Nov/19 Commented by $@ty@m123 last updated on 18/Nov/19 $${I}\:{tried}\:{to}\:{send}\:{you}\:{a}\:{book}\:{but}\:{the}\:{above} \\ $$$${number}\:{is}\:{not}\:{recognised}\:{by}\:{whatsapp}. \\ $$$${Are}\:{you}\:{from}\:{Ivory}\:{coast}? \\ $$ Commented by…
Question Number 74040 by Learner-123 last updated on 18/Nov/19 $${Find}\:{orthogonal}\:{trajectories}\:{of}\:{the} \\ $$$${curves}:\:\left({x}−{c}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} ={c}^{\mathrm{2}} . \\ $$ Commented by Learner-123 last updated on 18/Nov/19 $${please}\:{help}……
Question Number 74041 by FCB last updated on 18/Nov/19 Commented by mathmax by abdo last updated on 18/Nov/19 $${let}\:{A}_{{n}} =\left(\mathrm{1}+\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}}\right)^{\frac{\mathrm{1}}{{sin}\left(\pi\sqrt{\mathrm{1}+{n}^{\mathrm{2}} }\right)}} \:\Rightarrow \\ $$$$\left.{ln}\left({A}_{{n}}…
Question Number 8503 by MNG last updated on 13/Oct/16 $${Q}.\:\mathrm{1}\:\:{sinA}+{sinB}+{sinC}\:=\:\mathrm{4}{cos}\frac{{A}}{\mathrm{2}}\:{cos} \\ $$$$\frac{{B}}{\mathrm{2}}\:{cos}\:\frac{{C}}{\mathrm{2}}\:. \\ $$$${Q}.\mathrm{2}\:\:{cosA}\:{cosB}\:−\:{cosC}\:=\:\mathrm{4}{cos}\frac{{A}}{\mathrm{2}}\:{cos}\frac{{B}}{\mathrm{2}} \\ $$$${cos}\frac{{C}}{\mathrm{2}}\:−\mathrm{1} \\ $$$$ \\ $$$${Q}.\mathrm{3}\:\:\frac{{sin}\mathrm{2}{A}+{sin}\mathrm{2}{B}+{sin}\mathrm{2}{C}}{{sinA}+{sinB}+{sinC}}\:=\mathrm{8}{sin}\:\frac{{A}}{\mathrm{2}} \\ $$$${sin}\frac{{B}}{\mathrm{2}}\:{sin}\frac{{C}}{\mathrm{2}} \\ $$$$ \\…
Question Number 74037 by akshaypalsra8@gmail.com last updated on 18/Nov/19 $$\int_{\mathrm{0}^{} } ^{\Pi/\mathrm{2}} {x}\mathrm{cos}^{{n}} {xdx}\:\:\:{by}\:{reduction}\:{formula} \\ $$ Answered by mind is power last updated on 18/Nov/19…
Question Number 8498 by Chantria last updated on 13/Oct/16 Commented by Rasheed Soomro last updated on 13/Oct/16 $$\frac{\mathrm{2a}^{\mathrm{2}} }{\mathrm{3a}+\mathrm{bc}}×\sqrt{\frac{\mathrm{1}}{\mathrm{b}+\mathrm{c}}}×\frac{\mathrm{18ab}}{\left(\mathrm{3b}\right)^{\mathrm{2}} −\mathrm{5c}} \\ $$$$=\frac{\mathrm{2a}^{\mathrm{2}} }{\mathrm{3a}+\mathrm{bc}}×\frac{\mathrm{1}}{\:\sqrt{\mathrm{b}+\mathrm{c}}}×\frac{\mathrm{18ab}}{\mathrm{9b}^{\mathrm{2}} −\mathrm{5c}} \\…
Question Number 139561 by physicstutes last updated on 28/Apr/21 $$\mathrm{Near}\:\mathrm{the}\:\mathrm{shore}\:\mathrm{a}\:\mathrm{fisherman}\:\mathrm{jumps}\:\mathrm{out}\:\mathrm{of}\:\mathrm{his}\:\mathrm{boat}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity} \\ $$$$\mathrm{of}\:\mathrm{5}.\mathrm{00}\:\mathrm{ms}^{−\mathrm{1}} \:\mathrm{and}\:\mathrm{lands}\:\mathrm{on}\:\mathrm{the}\:\mathrm{shore}\:\mathrm{0}.\mathrm{650}\:\mathrm{afterwards}.\mathrm{The}\:\mathrm{boat} \\ $$$$\mathrm{moves}\:\mathrm{backwards}.\:\mathrm{The}\:\mathrm{respective}\:\mathrm{masses}\:\mathrm{of}\:\mathrm{the}\:\mathrm{fisherman}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{boat}\:\mathrm{are}\:\mathrm{85}.\mathrm{0}\:\mathrm{kg}\:\mathrm{and}\:\mathrm{165}\:\mathrm{kg}\:\mathrm{and}\:\mathrm{the}\:\mathrm{frictional}\:\mathrm{force}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{boat}\:\mathrm{and}\:\mathrm{water}\:\mathrm{is}\:\mathrm{negligible}.\:\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{fisherman}\:\mathrm{and}\:\mathrm{the}\:\mathrm{both}\:\mathrm{at}\:\mathrm{the}\:\mathrm{instant}\:\mathrm{when}\:\mathrm{he}\:\mathrm{just}\:\mathrm{lands}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{shore}? \\ $$…
Question Number 74026 by mathmax by abdo last updated on 17/Nov/19 $${U}_{{n}} {is}\:{a}\:{sequence}\:{wich}\:{verfy}\: \\ $$$$\forall{n}\:\in{N}\:\:\:\:\:\:\:\:\mathrm{2}^{{n}} \left(\:{U}_{{n}} +{U}_{{n}+\mathrm{1}} \right)=\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{is}\:\left({U}_{{n}} \right)\:{cojverhent}\:? \\…
Question Number 139560 by Dwaipayan Shikari last updated on 28/Apr/21 $$\underset{{n}_{\mathrm{1}} +\mathrm{2}{n}_{\mathrm{2}} +\mathrm{3}{n}_{\mathrm{3}} +..+{rn}_{{r}} ={n}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{n}_{\mathrm{1}} !{n}_{\mathrm{2}} !{n}_{\mathrm{3}} !..{n}_{{r}} !\mathrm{1}^{{n}_{\mathrm{1}} } \mathrm{2}^{{n}_{\mathrm{2}} } \mathrm{3}^{{n}_{\mathrm{3}}…